DASC 500: Introduction to Data Analytics

Statistical Inference (Part 1 - Concepts)

Maj Jason Freels PhD

22 January 2020

Overview

Introduction to Statistical Inference

Estimation

Hypothesis Testing

Motivating Example

Building Widgets

A random sample of five of our 'not-too-exciting' widgets

A random sample of five of our ‘not-too-exciting’ widgets

Assessing Uncertainty

Making inferences

Random Samples

Defining terms



Incorrect wording: \(n\) independent realizations of the random variable \(X\)

Correct wording: realizations of \(n\) independent random variables \(X_1,\ldots,X_n\)

Example 1: Independent and Identically Distributed

\[ F_{_{\Xi}}(\xi) = F_{_{X}}(x_1)\times\ldots\times F_{_{X}}(x_n) \]

Example 2: Identically Distributed, but not Independent

Statistical Estimation

Overview

Statistical Models

Point Estimates

Properties of point estimates

Methods to compute point estimates

Interval Estimates

Confidence Intervals

Confidence Level

Margin of Error

Hypothesis Testing

Overview

Hypothesis Testing Steps

Specialized Parametric Hypothesis tests

Summary

In this presentation

In the next presentation